id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
9,392 | y^2 = y^2 - 4y + 4 + 4y + 4(-1) = (y + 2(-1))^2 + 4y + 4(-1) |
1,033 | \frac12*((-1) + 1 + k*2) = k |
30,635 | 85/2 = \frac16\cdot 255 |
-1,129 | 8/1\cdot (-\frac12) = \dfrac{1}{1/8}\cdot \left(\left(-1\right)\cdot 1/2\right) |
-24,118 | \left(1 + 9\right)^2 = 10 \cdot 10 = 10^2 = 100 |
20,499 | 0 \gt \sin(\alpha)\Longrightarrow \alpha = -\tfrac{\pi\cdot 2}{3}\cdot 1 |
55,859 | 1 = 0^0 |
37,092 | \dfrac{1}{x^2 + 4\cdot \left(-1\right)}\cdot (x + 2\cdot (-1)) = \frac{x + 2\cdot (-1)}{\left(x + 2\cdot (-1)\right)\cdot \left(x + 2\right)} = \frac{1}{x + 2} |
-24,650 | -\frac{1}{10}\cdot 3 + 1/4 + 3/5 = 11/20 |
-1,282 | \left((-1)*1/3\right)/(7*1/8) = 8/7 (-\dfrac13) |
-5,117 | \dfrac{0.82}{100} = \frac{1}{100} \cdot 0.82 |
37,628 | |(-1) (-1) + x| = |x + 1| |
13,670 | |1/(z_1) - \frac{1}{z_2}| = |(-z_2 + z_1)/(z_2\cdot z_1)| |
31,928 | 2*(1 + 2 + \dots*n) = (n + 1)*n |
33,370 | 24 = 2^2\cdot {4 \choose 2} |
8,968 | -\frac{1}{2} \cdot \cos(2 \cdot \theta) + 1/2 = \sin^2(\theta) |
8,875 | \cos(x + z) = -\sin{z} \sin{x} + \cos{z} \cos{x} |
12,487 | \tan^{-1}(\infty)*4 = \pi*2 |
7,636 | (n + 1)^2 = 1 + 3 + 5 + \dotsm + n\cdot 2 + 1 |
-20,715 | \frac{1}{24 \cdot k} \cdot (6 + 27 \cdot k) = 3/3 \cdot \frac{1}{k \cdot 8} \cdot (k \cdot 9 + 2) |
-1,819 | 19/6 \pi - \pi\cdot 2 = \pi \frac76 |
19,511 | \frac{50}{2} \cdot \frac{1}{100} = \frac{1}{2 \cdot 2} = \tfrac14 |
-26,401 | z^k z^m = z^{m + k} |
-23,125 | -1/2*5/8 = -5/16 |
-9,137 | -p^2\times 42 - p\times 63 = -p\times 2\times 3\times 7\times p - p\times 3\times 3\times 7 |
-20,576 | -\frac85*\frac{2*x + 2*(-1)}{2*x + 2*(-1)} = \frac{-16*x + 16}{10*(-1) + x*10} |
22,067 | \frac{\Delta*z_2}{\Delta*z_1} = \frac{z_2*\Delta}{z_1*\Delta} |
-2,155 | π/2 + π*\frac16*11 = 7/3*π |
-20,553 | \frac{1}{z \times 80} \times ((-56) \times z) = -\frac{1}{10} \times 7 \times \dfrac{z \times 8}{z \times 8} \times 1 |
9,877 | \dfrac{1}{15} = \dfrac{1/20}{3 \cdot 1/4} |
2,952 | \frac{2 x y}{x + y} = \dfrac{2}{\frac{1}{x} + \frac1y} \leq \tfrac12 (x + y) |
27,614 | (1 + 0.5 + 0.5^2)\cdot 305 = 305 + (1 + 0.5)\cdot 305\cdot 0.5 |
24,959 | \frac34 = \frac{1}{2} \cdot \tfrac{3}{2} |
-7,619 | 10/5 - \dfrac{i*10}{5} = (10 - i*10)/5 |
-14,545 | 4*(6 + 3) = 4*9 = 36 |
7,007 | c = h \cdot l,b = h \cdot n\Longrightarrow \left(l \pm n\right) \cdot h = c \pm b |
44,540 | π = \frac{π}{2} + \dfrac{π}{2} |
-20,917 | \dfrac{48 \cdot x + 64}{x \cdot 18 + 24} = 8/3 \cdot \frac{1}{8 + 6 \cdot x} \cdot (x \cdot 6 + 8) |
23 | \|\frac{1}{\frac1A}\|*\|\frac1A\| = \|\frac1A\|*\|A\| |
28,699 | (x + 1) (4(-1) + x) = 4(-1) + x^2 - x*3 |
-19,071 | \frac{1}{3}2 = \frac{Y_x}{64 \pi} \cdot 64 \pi = Y_x |
8,951 | \left(\left(I = o \cdot A \Rightarrow A \cdot o \cdot A = I \cdot A = A\right) \Rightarrow \frac{A}{A} = \frac1A \cdot o \cdot A^2\right) \Rightarrow I = A \cdot o |
5,821 | 0 = -25 \cdot \frac{55}{25} + 80 + 25 \cdot (-1) |
-2,984 | \sqrt{7} \sqrt{9} + \sqrt{25} \sqrt{7} = 5 \sqrt{7} + \sqrt{7} \cdot 3 |
-23,720 | \tfrac{3}{7} \cdot 4/5 = 12/35 |
36,904 | x^{91} = \left(x^7\right)^{13} |
43,239 | 5 \cdot 8 \cdot 8 = 320 |
29,345 | 4^2 + 3^2 = 0^2 + 5^2 |
-20,719 | \frac{1}{30 \cdot \left(-1\right) + z \cdot 10} \cdot (-z \cdot 9 + 27) = \dfrac{1}{z + 3 \cdot (-1)} \cdot (3 \cdot \left(-1\right) + z) \cdot (-\dfrac{9}{10}) |
51,863 | \sum_{m=1}^\infty (\frac12 + (-1)^m)/m = \sum_{m=1}^\infty \tfrac{1}{2 \times m} + \sum_{m=1}^\infty (-1)^m/m = \left(\sum_{m=1}^\infty 1/m\right)/2 + \sum_{m=1}^\infty \frac1m \times (-1)^m |
2,456 | k + (-1) + y^l = (k + (-1))*\left(y^{l + \left(-1\right)} + \dotsm + y + 1\right) |
18,064 | 1 + z^2 + z*2 = z^2 + 3(-1) + 2z + 4 |
3,007 | \left((a + f)^2 - 4\cdot a\cdot f\right)^{1/2} = ((a - f) \cdot (a - f))^{1/2} = |a - f| |
-20,680 | \frac{1}{-8 \cdot \varphi + 2 \cdot (-1)} \cdot (-\varphi \cdot 3 + 7 \cdot (-1)) \cdot 3/3 = \frac{1}{-24 \cdot \varphi + 6 \cdot (-1)} \cdot (-9 \cdot \varphi + 21 \cdot (-1)) |
30,946 | \dfrac{x_0}{x_1} = \dfrac{1}{x_1}x_0 |
6,059 | \tfrac{1}{3 + 2\cdot k}\cdot (\left(-1\right) + k\cdot 2) = -\frac{4}{2\cdot k + 3} + 1 |
-23,449 | \dfrac{1}{21} \cdot 10 = 2/3 \cdot \frac{1}{7} \cdot 5 |
3,929 | 2 + 6*k = 3*2*k + 2 |
-15,825 | 0 = 5*5/10 - 5/10*5 |
-26,629 | (4 \cdot z)^2 - (7 \cdot y)^2 = (z \cdot 4 - y \cdot 7) \cdot (4 \cdot z + 7 \cdot y) |
26,153 | 1 - y/c = \frac{1}{c}\times (-y + c) |
-20,997 | \dfrac{1}{r \cdot 8}(-r \cdot 4 + 12 (-1)) = \tfrac{1}{2r}(3\left(-1\right) - r) \cdot 4/4 |
51,005 | e/2 - e^2/4 + \frac{e^3}{6} - \dots = \sum_{\omega=1}^\infty (-1)^{\omega + (-1)}\cdot e^\omega/(2\cdot \omega) = \sum_{\omega=0}^\infty (-1)^\omega\cdot \frac{e^{\omega + 1}}{2\cdot (\omega + 1)} |
9,846 | z - -f = z + f |
12,047 | 2 2 (2 + 1)^2/4 = 36/4 = 9 |
24,547 | 2 + 12\cdot k = k\cdot 5 + 1 + k\cdot 7 + 1 |
17,819 | 3 - 2\cdot g = g + d + e - 2\cdot g = -g + d + e |
14,858 | \dfrac{1}{dx^2} \cdot dy^2 = (\frac{1}{dx} \cdot dy)^2 |
-19,998 | \frac{9}{1} \frac{3 - 9n}{3 - 9n} = \frac{-n\cdot 81 + 27}{3 - n\cdot 9} |
-17,681 | 64*\left(-1\right) + 89 = 25 |
1,302 | \sin(s\cdot 2) = \cos\left(s\right)\cdot \sin(s)\cdot 2 |
13,074 | \frac{2/4\cdot \frac{3}{5}}{3} = \frac{1}{10} |
-27,383 | 379\times (-1) + 960 = 581 |
11,244 | \tfrac{1}{4} + (-1) = -\frac34 |
-2,156 | \dfrac{\pi}{6} - 5/3\cdot \pi = -\pi\cdot 3/2 |
27,946 | \cot(z) - \tan(z) = \frac{\cos(2\cdot z)}{\sin\left(2\cdot z\right)}\cdot 2 = 2\cdot \cot\left(2\cdot z\right) |
-20,383 | -4/9 \times \frac{1}{9 \times (-1) + x} \times (x + 9 \times (-1)) = \dfrac{36 - 4 \times x}{9 \times x + 81 \times (-1)} |
11,279 | d/dy \sin(y) = 2\cdot \cos(y)\cdot \pi |
29,556 | ((-1)\cdot \pi)/2 = -\frac{1}{2}\cdot \pi |
44,697 | 21*7 = 147 |
-5,468 | \frac{1}{20 (-1) + 4 x} = \frac{1}{4 (5 \left(-1\right) + x)} |
3,065 | 2 - \frac{2}{3 - x} = \frac{1}{3 - x}\cdot (4 - 2\cdot x) = \frac{1}{3 - x}\cdot 2\cdot (2 - x) |
17,979 | \frac{1 - \frac{D}{-d + f}}{\tfrac{D}{f - d} + 1} = \frac{f - d - D}{f - d + D} |
26,417 | f_1^2 - f_2 f_1 + f_2^2 = (f_1 - f_2)^2 + f_1 f_2 |
19,453 | \cos(\theta) - i\cdot \sin(\theta) = \cos\left(-\theta\right) + \sin(-\theta)\cdot i |
-713 | ({ e^{5\pi i / 3}}) ^ {15} = e ^ {15 \cdot (5\pi i / 3)} |
-12,056 | \frac{9}{10} = \frac{t}{20 \cdot \pi} \cdot 20 \cdot \pi = t |
33,171 | 2*2 = 2 * 2 |
15,718 | \frac{5!}{2!*2!} = \frac14*120 = 30 |
32,541 | -1/8 + 1/2 + \frac{1}{4} = \dfrac{1}{8}\cdot 5 |
18,357 | 73 = \left(19 - 2^{1/2}\cdot 12\right)\cdot (19 + 2^{1/2}\cdot 12) |
-9,454 | -15 \cdot n + 35 \cdot (-1) = -7 \cdot 5 - n \cdot 3 \cdot 5 |
-19,890 | 0.01 (-93) = -\frac{93}{100} = -0.93 |
28,335 | \sqrt{a^2 \cdot \sinh^2{p} + a^2} = a \cdot \sqrt{\sinh^2{p} + 1} = a \cdot \cosh{p} |
571 | \binom{2^n}{2} + (-1) = \frac{1}{2}\cdot 2^n\cdot (2^n + (-1)) + (-1) = \frac12\cdot (2^{2\cdot n} - 2^n + 2\cdot (-1)) |
7,012 | 1/(u\frac{x}{u}) = u\frac{1}{ux} |
10,355 | h^2 = (k + 3 (-1)) (k + 3 (-1)) + (h + 4 (-1))^2 \implies (k + 3 (-1))^2 = h h - (h + 4 (-1))^2 = 8 h + 16 \left(-1\right) = 8 (h + 2 \left(-1\right)) |
-9,356 | s\cdot 10 + 50\cdot (-1) = 2\cdot 5\cdot s - 2\cdot 5\cdot 5 |
1,553 | y_1 + i\cdot y - y_2 + i\cdot k = y_1 - i\cdot y + \left(y_2 - i\cdot k\right)\cdot (y_1 - y_2) + y - k = y_1 + y_2 - y - k |
-20,891 | -9/4 \cdot \frac{7 \cdot (-1) - 8 \cdot l}{-8 \cdot l + 7 \cdot (-1)} = \frac{l \cdot 72 + 63}{-32 \cdot l + 28 \cdot \left(-1\right)} |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.